
Journal of Convex Analysis 21 (2014), No. 1, 189200 Copyright Heldermann Verlag 2014 Some Geometric Properties of the Cesàro Function Spaces Damian Kubiak Mathematics Department, Tennessee Technological University, 110 University Drive, Box 5054, Cookeville, TN 38505, U.S.A. dkubiak@tntech.edu [Abstractpdf] Some geometric properties of the Ces{\`a}ro function spaces $C_{p,w}$, $1\leqslant p<\infty$, induced by an arbitrary positive weight function $w$ on an interval $(0,l)$ where $0 < l \leqslant\infty$ are studied in this paper. It is shown that all nonempty relatively weakly open sets in the unit ball of $C_{p,w}$ have diameter $2$. Also $C_{p,w}$, $1<p<\infty$ is strictly convex but no point of its unit ball is strongly extreme. Moreover, some connections between uniformly nonsquare points and various geometric properties in general Banach spaces are presented. Keywords: Cesaro function space, diameter 2 property, weak neighborhoods, uniformly nonsquare points. MSC: 46E30, 46B20, 46B42 [ Fulltextpdf (146 KB)] for subscribers only. 